The invention relates generally to dielectric materials in which the constituent dielectric properties can be adjusted by optical control. In particular, this invention relates to techniques for producing a dynamically controllable artificial dielectric (AD).
Composite dielectrics are of high interest because their electromagnetic properties can be controlled synthetically. In particular, the method of mixing several dielectric components together to achieve a final effective permittivity is useful for many electromagnetic applications and examples have been around for more than a century. As one example, there may be a need for a particular permittivity to obtain a specific electromagnetic impedance to minimize radio frequency (RF) reflection.
A composite material in which at least one of the components is a good conductor is referred to as an artificial dielectric as coined by W. E. Kock, “Metallic delay lenses,” Bell Systems Technical Journal, 27 (1), 59-82 (January 1948). The term “artificial dielectric” is used to distinguish the polarization properties of a conductor from that of an insulating dielectric. The conductor consists of what is known to those skilled in the art as “free” charge whereas a dielectric insulator consists of “bound” charge. Either achieves a similar polarization response to an applied electric field. A dynamic photo-variable dielectric response can be realized by using a photo-conductive material as a component in the composite dielectric (H. Kallman et al., “Induced conductivity in luminescent powders. II. AC impedance measurements,” Phys. Rev., 89 (4) 700-707, February 1953). The dielectric permittivity constant of a photo-conductive material as a first component (component-1) can be represented by the complex relation:
                              ɛ          p                =                              ɛ            p            ′                    -                      j            ⁢                          σ              ω                                                          (        1        )            
where ∈′p is the real part of the permittivity, j=√{square root over (−1)} is the imaginary number, σ is the photo-conductivity, ω is the angular frequency and the subscript p means photo-conductive particulate. In eqn. (1), the imaginary component stems only from conductivity and is assumed to be much larger than from other dielectric loss effects.
For the case of a two-element material, the permittivity of the second component (component 2) can be represented simply as ∈b, where the subscript b refers to an insulating binder. Here the second component is treated as an insulator and so has conductivity of zero, i.c.,∈b=∈′p.  (2)
Many dielectric mixing equations exist depending on geometrical and material parameters. One popular mixing equation known by those artisans of ordinary skill is the Lichtenecker equation (K. Lichtenecker: “Die Dielektrizitäts-konstante natürlicher and kunstlicher Mischkörper,” Physik. Zeits. 27, 1926) given by:∈=∈1f1∈21-f1  (3)where f1 is the volumetric fill factor of component-1. Note that eqn. (3) is written for a two-component composite dielectric, but can be extended to multiple components (R. Simpkin: “Derivation of Lichtenecker's Logarithmic Mixture Formula from Maxwell's Equations,” IEEE Trans. Microwave Theory Tech., 58 (3) 545-550, March 2010.). This equation is generally appropriate for mixtures that are symmetric, meaning that geometrically the particles can be interchanged and the equation remains valid.
For the case that the photo-conductive component is within an insulating binder material, then another relation has been shown to be effective from Kevin A. Boulais et al.: “Optically Controllable Composite Dielectric Based on Photo-conductive Particulates”, IEEE Trans. Microwave Theory and Techniques, 62 (7), 1448-1453 (June, 2014).
                              ɛ          e                =                                            ɛ              b                        ⁢                          ⌊                                                ɛ                  b                                +                                                      (                                                                  ɛ                        p                                            -                                              ɛ                        b                                                              )                                    ⁢                                      f                                          2                      /                      3                                                                                  ⌋                                                          ɛ              b                        +                                          (                                                      ɛ                    p                                    -                                      ɛ                    b                                                  )                            ⁢                              (                                                      f                                          2                      /                      3                                                        -                  f                                )                                                                        (        4        )            In eqn. (4) the materials are not symmetric as might be the case for conducting particulates and an insulating and otherwise continuous binder.